# How do you solve the system of equations 5x - 6y = 9 and 5x + 2y = 19?

Mar 22, 2017

The final solution is $x = 3 \frac{3}{10}$ and $y = 1 \frac{1}{4}$ using substitution to solve the system of equations.

#### Explanation:

We notice that in both equations, there is a $5 x$. This suggests using elimination to solve the equations.

Since the equations have the same term with one of the variables ($5 x$), we can subtract the two equations to eliminate $x$ and leave one equation to solve for $y$. Subtracting the first equation from the second and solving gives us:

$2 y - \left(- 6 y\right) = 19 - 9$

$8 y = 10$

$y = \frac{5}{4}$

Now, we can simply substitute the value of $y$ into any of the 2 equations to solve for $x$. Substituting into the second equation and solving, we get:

$5 x + 2 \left(\frac{5}{4}\right) = 19$

$5 x + \frac{5}{2} = 19$

$5 x = \frac{33}{2}$

$x = \frac{33}{10}$

So, the answer to the equations is $x = 3 \frac{3}{10}$ and $y = 1 \frac{1}{4}$.